Acoustoelectric (AE) imaging provides electro-anatomical contrast by mapping the distribution of electric fields in biological tissues, by delivering ultrasound waves which spatially modulate the medium resistivity via the AE effect. The conventional method in AE imaging is to transmit focused ultrasound (FUS) beams; however, the depth-of-field (DOF) of FUS-AE is limited to the size of the focal spot, which does not span across the centimeter-scale of organs. Instead of fixing the focal depth on transmission, we propose to dynamically synthesize the AE modulation regions via a Synthetic Aperture approach (SA-AE). SA-AE involves a straightforward pixel-based delay-and-sum reconstruction of AE images from unfocused AE signals. In saline and ex vivo lobster nerve experiments, FUS-AE was shown to perform well only at the focal depth, with poor spatial resolution for out-of-focus electric sources. Meanwhile, SA-AE generally improved spatial resolution throughout the DOF, but introduced strong background noise. The flexibility of uncoupled, single-element induced AE signals in SA-AE was further leveraged to quantify their spatial coherence across the transmit aperture, obtaining maps of the coherence factor (CF) and pulse-length coherence factor (CFPL). Weighting SA-AE images with their derived CF and CFPL maps resulted in further improvement in image resolution and contrast, and notably, boosted the image SNR beyond that of FUS-AE. CFPL exhibited stronger noise suppression over CF. Using unfocused wave transmissions, the proposed coherence-weighted SA-AE strategy offers a high resolution yet noise-robust solution towards the practical imaging of fast biological currents.